Reasoning · Grade 4-2 Transformations and Angles
Problem
Order the rays and name the five gaps.
Putting the rays in order first turns a messy overlap picture into a simple line-up, and then each square is just a pair of positions in that line-up.
4.G.A.1Draw A DiagramLining the six rays up in order turns the tangle into five gaps that can be added and subtracted.
Angles that sit side by side around one point combine exactly like lengths laid end to end.
Each gap sits between exactly one pair of neighbouring rays, so six rays in order give five gaps and no more.
Each square gives one 90-degree equation.
The only thing a square contributes at its corner is a right angle, and a big angle is just the sum of the smaller angles packed inside it — so each square turns into one short addition sentence.
4.G.A.2Identify SubproblemsThe first gives the first two summing to 45 degrees.
Even without knowing either angle by itself, knowing their total is real progress — and it is exactly the chunk that appears again in the next sentence.
4.MD.C.7Identify SubproblemsFeeding that into the second gives the third as 45 degrees.
Swapping a known chunk in for two unknowns turns a sentence with three unknowns into one with a single unknown — the same trick as replacing '2 + 3' by '5' in an addition.
4.MD.C.7Organize Information In More WaysThe third equation gives 20 degrees.
Once one unknown is pinned down, the sentence it shares with the next unknown becomes a one-step subtraction.
4.MD.C.7Identify SubproblemsComing back, the first is 25 degrees.
The chunk that was parked in step 3 comes back into play at the end, so nothing found along the way was wasted.
4.MD.C.7Identify SubproblemsEvery square corner is exactly 90° — so each square in the pile becomes one simple addition sentence, and the unknowns pop out one at a time.